For level and flow control, they are generally about 10 to 15 percent. For restoring normal conditions in a distillation column, the margin for reflux control may be even higher at 20 percent. The maximum for the control valve will therefore be 110 to 120 percent of the design, depending on the nature of the corrective action. Most processes are expected to operate at 100 percent of design capacity for the best overall efficiency. However, they may have to be designed for operation at lower than 100 percent also. This lower flow capacity may occur for significant periods of time. Limitations of feed availability or product off take may force the operator to run the process at low loads.

Generally, the turndown condition is defined during design so that all the components of the process are selected accordingly. The turndown condition in this case is to be treated as an alternate operating condition, from a control point of view. A margin below the turndown is required for the same reasons as the margin above the maximum flow. A temporary, high level in a boiler drum may have to be restored to normal by reducing the intake flow of the drum during turndown operation of the process. Therefore, the control valve’s minimum flow has to be computed considering about 10 to 20 percent below that needed for a steady state turndown condition of the plant, with the margin depending on the nature of the corrective action needed. The extreme maximum and minimum flows defined above with the margins should be matched to a control valve’s usable limits of 90 and 10 percent openings, respectively, to make best use the valve’s capabilities while also ensuring that the control valve is not forced to operate outside its recommended opening.

Using the control valve from Equation 1 for the minimum and maximum flow rates, a relationship between the control valve (∆P) at minimum flow and the ∆P at maximum flow can be created. For valves with linear characteristics, the relationship is shown in Equation 3. ΔP_{minflow}/ΔP_{maxflow} = [(0.90 x F_{minflow}) / (0.10 x F_{maxflow})] ^{2} (Equation 3)

## System and Control Valve

A common practice in pump systems is to allow a minimum of 10 to 15 psi for the control valve’s pressure drop. Using Equation 3 and the control valve pressure drop at maximum flow, the designer can calculate the control valve pressure drop at minimum flow and at normal (100 percent) flow. The system head and the control valve head for minimum and maximum flow are shown in Figure 3. The straight lines are based on a case in which the maximum flow is 115 percent and the control valve head loss is 10 meters of water column (WC). Lines for different minimum flow cases (30 percent L, 35 percent L, 40 percent L, 45 percent L and 50 percent L) are also plotted.

In a pump and control valve system, these lines should always fall on the characteristic curve of a centrifugal pump since the system head plus control valve loss has to equal the pump head. However, some of these lines can be seen to slope downward toward lower flow rates, which is unlike the shape of a centrifugal pump curve, which slopes down toward rising flow conditions. Depending on the shape of the pump curve, only one of these lines will best match the pump curve. In Figure 3, at 45 percent and higher minimum flow, the head requirement is seen to reduce with increased flow. In a second example, the above computations are based on a control valve with 30 meters of WC loss at maximum flow, instead of 10 meters of WC loss considered earlier. Loss at minimum flow is computed following the above steps. These lines (30 percent H, 35 percent H, 40 percent H, 45 percent H and 50 percent H) are also plotted in Figure 3. With these plots, even for the 30-percent turndown case, the head reduces with increased flow. The system head plus control valve head in this case will track the pump curve even to a lower value of minimum flow than was seen with the 10-meter WC head loss control valve.

## Pump Characteristics

The impact of the flow turndown requirement on pump duty can be evaluated if the shape of the pump curve is known. A parabolic type pump characteristic curve developed using Equation 4 is considered for further study. H_{pump} = a + b x flow + c x flow^{2} (Equation 4) Where: a, b and c are constants For a typical pump, a family of pump curves will exist. The flow versus head relationship depends on the diameter of the impeller and can be calculated using the law of affinity shown in Equation 5. H_{pump} = (a + b x flow + c x flow^{2}) x n^{2} (Equation 5) Where: n = the ratio of the impeller diameter, such as n = D_{2}/D_{1}

The curve with minimum n that meets the system plus control valve head, at minimum, normal and maximum flow conditions represents the optimum pump selection. These curves are plotted on Figure 4 showing 25.6 percent, 28.8 percent, 32.9 percent, 38.3 percent, 46.0 percent and 57.5 percent minimum flow cases with 115 percent as the maximum flow in all the cases. This is accomplished by simultaneous solution of the system head (Equation 2), control valve (Equation 3) and pump family of curves (Equation 5) to calculate a diameter ratio, n. The constants used for the pump curve were a = 200, b = -0.05 and c = -0.001.